Quasiclassical Surface of Section Perturbation Theory

Abstract

Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This solves the long standing problem of quantizing the resonances and chaotic regions generically appearing in classical perturbation theory. The result is achieved by expanding the `phase' of the wavefunction in powers of the square root of the small parameter. It gives explicit WKB-like wavefunctions even for systems which classically show hard chaos. We also find analytic solutions to some questions raised recently.